Study On Measuring Optical Properties Of Solids With Reflection Electron Energy Loss Spectroscopy

1st ChapterOptical property, as one of the most important basic physical properties of a solid,has been a hot research topic in material study at different scales and dimensions. The optical constants, on the one hand, reflect the response of the material to the external macro electric field. They connect the relationship between the total electric field E and the local electric field Eloc with a math relationship. On the other hand, the response to the light of different wavelengths contains rich information of the microscopic quantum-states of a solid, such as light-phonon and electron-phonon interactions in the infrared range, intraband and interband transitions, exciton excitations and the plasmonic exci-tations of light in the visible and vacuum ultraviolet range, as well as the inner shell ionization process in the higher energy range of x-ray. Experimentally, whether it is macroscopically studying the polarization properties of the material, or microscopically studying the excitations of an electron from low energy level(or band) to higher energy level(or band), we can either use photons or electrons as a probe to study the optical constants of the material. In this chapter we start from the basic electromagnetic theory to introduced the basic theory of optical constants. Later we deduce the relationship between dielectric functions felt by incident photons and electrons.On this basis, we introduce the current photon and electron based measurements of optical constants. Fi-nally, we put emphasis on the current progress of using reflection electron energy loss spectroscopy in measuring the optical constants, by which we propose the motivation of our study in this thesis.2nd ChapterThis chapter introduces the scattering theory of electrons in materials and the com-monly used methods for deriving optical constants from electron energy loss spec-troscopy. This includes the topics of the elastic and inelastic scattering theory of elec-trons, the multiple scattering description methods of electrons and related global opti-mization algorithms. In the experiments of electron energy loss spectroscopy, electrons experience complex type of interactions with the material after taking off to get inside a material to the time when it is finally received by the collector. For fast electrons, these types of interactions contains (1) the elastic scattering from the ion core formed by the nuclei and the screening electrons of the material, which mainly results in deflections of a moving electron under the Coulomb interactions. In this part we introduced some common models of elastic scattering, including the well-known shielded Rutherford scattering cross sections and the accurate Mott cross sections. (2) The interactions be-tween the incident electrons and the electrons outside the nucleus, contains two types of common excitation types, namely, single electron excitations and collective excitations.For inelastic scattering, we first introduce the full-Penn method for the electron energy loss function, the single-pole approximation method and Ritchie and Howie's dielectric function model. Then we display the inelastic scattering cross section formula and the derivation process for infinite materials and semi-infinite materials, where we put stress on the surface excitation contributions of a real sample. In addition, this chapter also in-troduces several major models for extracting optical constants from reflection electron energy loss spectroscopy, including the Tougaard-Chorkendorff method, the extended-Landau method, the double fourier series convolution method of Werner and the Yubero method. Finally we introduce the Monte Carlo method and some global optimization algorithms in the Reverse Monte Carlo(RMC) method.3rd ChapterThe inelastic scattering process of electrons in a material plays a key role for sur-face analysis techniques based on surface electron spectroscopy (such as x-ray photo-electron spectroscopy XPS and Auger electron spectroscopy AES). We know that there is a close association between the inelastic scattering of electrons and the energy loss function (ELF) of a materia. For infinite media, ELF are proportional to the inelastic scattering probability of electrons moving in a material, which determines the energy loss and angle distribution of an electron after inelastic scattering. The energy loss function Im[-1/?(?, q)] of electrons is a bivariate function of energy losshw and mo-mentum transferhq, which in essence comes from the probability statistics of various excited states of the energy bands of a material. Thus it characterizes the inelastic scat-tering properties of the electrons. In the first chapter, we have proved that the optical energy loss function and the electron energy loss function equal in the case ofhq = 0.For the case of momentum transfer being non-zero, it is necessary to use an appropriate dielectric function model to extrapolate the optical energy loss function. In this chapter,we use the methods proposed by Ritchie and Howie, where we use certain number of Drude-Lindhard oscillators to fit the experimental energy loss functionsIm[-1/?(?,q)]of 26 kinds of materials and later we extrapolate them to the electron energy loss func-tionIm[-1/?(?,q)]. In the content of this chapter, we selected appropriate experimental data to obtain the energy loss function of 26 kinds of materials by using the sum rule check. On this basis, we fitted the Drude-Linhard oscillator parameters of the 26 mate-rials, in order to facilitate the field of surface electron spectroscopy research. Finally as an application of the Drude-Linhard parameters, the simulation of the REELS spectrum of Ag is given.4th ChapterIn this chapter, we mainly introduce the principle of the RMC method. By the application of several transition metals, we confirmed its accuracy and reliability. In the application of Fe materials, we obtained the energy loss functions of Fe at 1000 eV,2000 eV and 3000 eV, where we confirm the energy loss function by the RMC method is independent of the incident energy, namely it satisfies theoretical self-constancy. Then we compared our results with the data in the literature, it is found that the energy loss function obtained by the RMC method agrees with the results of DFT calculation, Pa-lik's optical measurement data, and Henke's X-ray absorption measurement in a wide range. Together We also obtained the inelastic mean free path of the Fe material in the 0-3000 eV range, where we point out the wrong result of the famous Tanuma-Powell-Penn (TPP-2M) formula. In addition, the RMC method is applied to the Ni material and we obtain the energy loss function, the optical constants and the dielectric function of Ni. Through comparative study of Werner's method, we pointed out that the results of Werner's method are inaccurate. Finally, based on the experimental REELS spectra of three materials of Cr, Co and Pd under three incident energies, the related ELFs are obtained, which shows the RMC method has good universality. Through detailed anal-ysis of the results of each material, we point out that the inaccuracy of Palik's energy loss function has an important source from the refractive index measurement.5th ChapterIn this chapter, we reviewed the extensive applications of lanthanide materials and the undeserved rareness of their optical constant data. Due to its active chemical proper-ties, optical measurements of Sm are very difficult and need a series of means to ensure the purity of the Sm sample during the measurement process. The RMC method we are developing is just in line with such measurement requirements. This chapter introduces the first measurement of the optical constants of Sm in the complete 0-100 eV region by the RMC method. We adopt the reflection electron energy loss spectrum of Sm mea-sured at 1000 eV and 2000 eV, and by applying the RMC method we obtained energy loss functions of each measurement. We found that the two energy loss functions show a large difference from 36-60 eV. By applying the sum rules, we confirmed that the 1000 eV REELS provides the accuracy results. The reason for the large error in the results from the 2000 eV spectrum can possibly be from the contributions of small amount of oxygen atoms remained in the sample. Finally, we compare the current results of Sm's optical data with few data in the literature, which partly proves the rationality of the Sm optical data measured by RMC.6th ChapterGraphene is a macromolecule composed of sp2 hybrid carbon atoms of the hon-eycomb structure which has thickness of a single atom . Since its discovery in 2004,and due to many of its unique quantum properties, graphene has attracted worldwide interests from the science Community. In this chapter we find that the energy spectra of 200 eV and 500 eV have more obvious characteristic structure of electron excitations by graphene after spectrum analysis of the reflection electron energy loss spectra measured at 200 eV, 500 eV and 2000 eV for a vacuum-monolayer graphene-bulk Ir substrate sample system. Then We constructed the inelastic scattering cross-section model of the three-phase sample system consisting of vacuum-monolayer graphene-bulk Ir substrate,upon which the reflection electron energy loss spectra of vacuum-monolayer graphene-bulk Ir substrate are simulated by the Monte Carlo method. At last, we compare the simulated electron energy loss spectrum with the experimental energy spectrum and recognize that the current model holds the possibility of measuring the optical proper-ties and dielectric properties of graphene in a wide range.